Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
Information retrieval (IR) is the activity of obtaining information system resources relevant to an information need from a collection. Searches can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for metadata that describe data, and for databases of texts, images or sounds.
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general.
Sir Charles Antony Richard Hoare, is a British computer scientist. He developed the sorting algorithm quicksort in 1959/1960. He also developed Hoare logic for verifying program correctness, and the formal language communicating sequential processes (CSP) to specify the interactions of concurrent processes and the inspiration for the occam programming language.
Ole-Johan Dahl was a Norwegian computer scientist. Dahl was a professor of computer science at the University of Oslo and is considered to be one of the fathers of Simula and object-oriented programming along with Kristen Nygaard.
In computer science, specifically software engineering and hardware engineering, formal methods are a particular kind of mathematically based technique for the specification, development and verification of software and hardware systems. The use of formal methods for software and hardware design is motivated by the expectation that, as in other engineering disciplines, performing appropriate mathematical analysis can contribute to the reliability and robustness of a design.
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph, in which the nodes represent transitions and places. The directed arcs describe which places are pre- and/or postconditions for which transitions. Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.
In computer science, model checking or property checking refers to the following problem: Given a model of a system, exhaustively and automatically check whether this model meets a given specification. Typically, one has hardware or software systems in mind, whereas the specification contains safety requirements such as the absence of deadlocks and similar critical states that can cause the system to crash. Model checking is a technique for automatically verifying correctness properties of finite-state systems.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
In computer science, concurrency refers to the ability of different parts or units of a program, algorithm, or problem to be executed out-of-order or in partial order, without affecting the final outcome. This allows for parallel execution of the concurrent units, which can significantly improve overall speed of the execution in multi-processor and multi-core systems. In more technical terms, concurrency refers to the decomposability property of a program, algorithm, or problem into order-independent or partially-ordered components or units.
Neil Immerman is an American theoretical computer scientist, a professor of computer science at the University of Massachusetts Amherst. He is one of the key developers of descriptive complexity, an approach he is currently applying to research in model checking, database theory, and computational complexity theory.
In computer science, formal specifications are mathematically based techniques whose purpose are to help with the implementation of systems and software. They are used to describe a system, to analyze its behavior, and to aid in its design by verifying key properties of interest through rigorous and effective reasoning tools. These specifications are formal in the sense that they have a syntax, their semantics fall within one domain, and they are able to be used to infer useful information.
Process architecture is the structural design of general process systems. It applies to fields such as computers, business processes, and any other process system of varying degrees of complexity.
Willibrordus Martinus Pancratius van der Aalst is a Dutch computer scientist and full professor at RWTH Aachen University, leading the Process and Data Science (PADS) group. His research and teaching interests include information systems, workflow management, Petri nets, process mining, specification languages, and simulation. He is also known for his work on workflow patterns.
Professor Martin C. Henson FBCS FRSA is an English computer scientist based at the University of Essex. He is Dean for International Affairs and is affiliated to the School of Computer Science & Electronic Engineering. Henson was Head of the Department of Computer Science from 2000–2006.
Grzegorz Rozenberg is a Polish Dutch computer scientist.
Rüdiger Valk is a German mathematician. From 1976 to 2010 he was Professor for Theoretical Computer Science (Informatics) at the Institut für Informatik of the University of Hamburg, Germany.
